Final answer:
The plant described is Azolla, a small aquatic fern that floats on water and can house nitrogen-fixing cyanobacteria.
Step-by-step explanation:
The free-floating plant with spongy, dusty-green leaves found in tropical and sub-tropical freshwater bodies is Azolla.
Azolla, also known as mosquito fern, is a small, floating aquatic fern that has very small leaves about 1 mm in size and can sometimes house nitrogen-fixing cyanobacteria. This symbiotic relationship with the cyanobacteria enables Azolla to increase rice yield substantially in rice paddies, serving as a natural nitrogen fertilizer.